Dynamics of a nonlocal phytoplankton species with nonlinear boundary conditions: Dynamics of a nonlocal phytoplankton

In this paper, a nonlocal reaction–diffusion–advection model with nonlinear boundary conditions arising from phytoplankton species is investigated, where the species depends solely on light for its metabolism. Firstly, we prove that a single phytoplankton model with nonlinear boundary conditions is...

Full description

Saved in:
Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2024, Vol.75 (6)
Main Authors: Li, Chaochao, Guo, Shangjiang
Format: Article
Language:English
Subjects:
Engineering
Mathematical Methods in Physics
Theoretical and Applied Mechanics
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, a nonlocal reaction–diffusion–advection model with nonlinear boundary conditions arising from phytoplankton species is investigated, where the species depends solely on light for its metabolism. Firstly, we prove that a single phytoplankton model with nonlinear boundary conditions is a strongly monotone dynamical system with respect to a non-standard cone related to the cumulative distribution functions, and further determine the global dynamics of single phytoplankton species in terms of boundary reaction functions. Secondly, we obtain the existence and uniqueness of positive steady states in terms of the critical death rate of the phytoplankton species by using the Lyapunov–Schmidt reduction method. Thirdly, we analyze the effects of advection rate, diffusion rate and water column depth on critical death rate under some conditions. Finally, we investigate the asymptotic behaviors of positive steady state for large advection rate.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-024-02362-0